PK 2017 Q18
18. Ivana has two identical dice and on the faces of each are the numbers −3, −2, −1, 0, 1, 2. If she throws her dice and multiplies the results, what is the probability that their product is negative?
- A \(\dfrac{1}{4}\)
- B \(\dfrac{11}{36}\)
- C \(\dfrac{1}{3}\)
- D \(\dfrac{13}{36}\)
- E \(\dfrac{1}{2}\)
Pink Kangaroo 2017, Question 18. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: C \(\dfrac{1}{3}\)
We can get a negative product if the first die is negative and the second positive, with probability \(\tfrac{3}{6} \times \tfrac{2}{6} = \tfrac{6}{36}\), or if the first die is positive and the second is negative, with probability \(\tfrac{2}{6} \times \tfrac{3}{6} = \tfrac{6}{36}\). Together this gives a probability of \(\tfrac{12}{36} = \tfrac{1}{3}\).
Solution © UK Mathematics Trust, from the PK 2017 solutions.